The young sigma Orionis cluster is an indispensable basis for understanding the formation and evolution of stars, brown dwarfs, and planetary-mass objects. Our knowledge of its stellar population is, however, incomplete. I present the Mayrit catalogue, which comprises most of the stars and high-mass brown dwarfs in the cluster. The basis of this work is an optical-near infrared correlation between the 2MASS and DENIS catalogues in a circular area of radius 30 arcmin centred on the OB-type binary sigma Ori AB. The analysis is supported by a bibliographic search of confirmed cluster members with features of youth and by additional X-ray, mid-infrared, and astrometric data. I list 241 sigma Orionis stars and brown dwarfs with known features of youth, 97 candidate cluster members (40 are new), and 115 back- and foreground sources in the survey area. The 338 cluster members and member candidates constitute the Mayrit catalogue. This catalogue is a suitable input for studying the spatial ditribution, multiplicity, properties and frequency of discs, and the complete mass function of sigma Orionis.